Apparatus and method for estimating a channel

ABSTRACT

An apparatus for estimating a channel from a transmitting point to a receiving point in an environment, in which at least two transmitting points spaced apart from each other are present, the transmitting point having associated therewith a pilot sequence, wherein the pilot sequences are different from each other, having a provider for providing an input signal, the input signal including a superposition of signals from the transmitting points, a multiplier for providing a number of copies of the input signal, the number of copies being equal to the number of transmitting points, for each copy of the input signal, a transformer for transforming the copy or a signal derived from the copy to obtain a transformed signal, the transformer being operative to apply a transform algorithm which is based on a Fourier transform, and for each transformed signal, an extractor extracting a portion of the transformed signal.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of copending InternationalApplication No. PCT/EP03/05376, filed May 22, 2003, which designated theUnited States, and is incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is in the field of telecommunications and, inparticular, in the field of channel estimation in a multiple inputscenario, in which a receiver receives signals from more than onetransmitting antenna.

2. Description of the Related Art

The steadily-increasing demand for high data rates necessary for today'sand future mobile radio applications require high data rate techniquesefficiently exploiting the available band width or, in other words, theachievable channel capacity. Therefore, multiple input multiple output(MIMO) transmission systems have achieved considerable importance inrecent years. MIMO systems employ a plurality of transmitting points,each of the transmitting points having a transmit antenna, and aplurality of receiving points, each of the receiving points having areceiving antenna, to receive signals being transmitted by the multipletransmitting points through different communication channels. In MIMOtechniques, where the signals impinging from several transmitterantennas need to be separated, space-time codes or special multiplexingmethods are used.

The signals impinging on each receive antenna are the superposition ofthe signals from N_(T) antennas, where N_(T) denotes a number oftransmitting points. This implies new challenges for channel estimation.Channel parameters, like a channel impulse response or a channeltransfer function are required for subsequent processing of the receiveddata. While the separation of the signals corresponding to severaltransmitting points, each of them having a transmit antenna, is achallenging task, the extension from a receiver having one antenna to asystem with several receive antennas is straight forward, as long as thesignals are mutually uncorrelated. The structure of the channelestimation units is independent of the number of receive antennas N_(R).The extension from a multiple input single output (MISO) system to aMIMO system is to employ N_(R) parallel channel estimation units, onefor each receiving point (receive antenna).

The use of coherent transmission techniques in wireless systems requiresestimation and tracking of the mobile radio channel. Since the signalstransmitted from multiple transmit antennas are observed as mutualinterference, channel estimation for MIMO systems is different from thesingle transmit antenna scenario. MIMO systems can be used with amulticarrier modulation scheme to further improve the communicationcapacity and quality of mobile radio systems. A prominent representativeof multi-carrier modulation techniques is the orthogonal frequencydivision multiplexing. (OFDM) technique.

Multi carrier modulation in particular orthogonal frequency divisionmultiplexing (OFDM) has been successfully applied to a wide variety ofdigital communication systems over the past several years. In particularfor the transmission of large data rates in a broadcasting scenario(e.g. digital TV), OFDM's superior performance in transmission overdispersive channels is a major advantage. OFDM has been chosen forvarious digital broadcasting standards, e.g. DAB or DVB-T. Anotherwireless application of OFDM is in high speed wireless local areanetworks (WLAN).

OFDM was first introduced in the 1960s. An efficient demodulationutilising the discrete Fourier transform (DFT) was suggested by S.Weinstein and P. Ebert, “Data Transmission by Frequency DivisionMultiplexing Using the Discrete Fourier Transform”, IEEE Transactions onCommunication Technology, vol. COM-19, pp. 628-634, October 1971. Byinserting a cyclic prefix into the guard interval (GI) longer than themaximum delay of the channel, inter-symbol interference (ISI) can beeliminated completely and the orthogonality of the received signal ispreserved. Since future mobile communication systems should support datarates several times higher than current systems, multi-carrier systemswith proper coding and interleaving offer both efficient implementationthrough the application of the Fast Fourier Transform (FFT) andsufficient robustness to radio channel impairments.

Another OFDM-based approach, termed multi-carrier code divisionmultiplex access (MC-CDMA), were spreading in frequency direction as hasbeen introduced in addition to the OFDM modulation, as described in K.Fazel and L. Papke, “On the Performance of Convolutionally-CodedCDMA/OFDM for Mobile Communication Systems”, in Proc. IEEE Int.Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'93), Yokohama, Japan, pp. 468-472, September 1993. MC-CDMA has beendeemed to be a promising candidate for the downlink of fourth generationsystems. Moreover, a MC/CDMA system with a variable spreading factor hasbeen proposed as described in H. Atarashi and M. Sawahashi, “VariableSpreading Factor Orthogonal Frequency and Code Division Multiplexing(VSF-OFCDM)”, in 3^(rd) International Workshop on Multi-CarrierSpread-Spectrum & Related Topics (MC-SS 2001), Oberpfaffenhofen,Germany, September 2001.

A block diagram of an OFDM system is shown in FIG. 4. For OFDM-basedMIMO systems, one OFDM modulator is employed on each transmitting point,while OFDM demodulation is performed independently for each receivingpoint. The signal stream is divided into N_(C) parallel sub-streams. Thei^(th) sub-stream commonly termed i^(th) sub-carrier of the l^(th)symbol block (OFDM symbol) is denoted by X_(l,i). After serial toparallel conversion (S/P) performed by a S/P converter 701 an inversediscrete Fourier transform (DFT) with N_(FFT) points is performed by anIFFT transformer 703 on each block and, subsequently, the guard interval(GI) having N_(GI) samples is inserted by a GI block 705 to obtain asignal x_(l,n) after parallel to serial (P/S) conversion performed by aP/S converter 703. After digital to analogue (D/A) conversion, thesignal x(t) is transmitted over a mobile radio channel with an impulseresponse h(t, τ). The received signal at receive antenna ν consists ofsuperimposed signals from NT transmitting points. Assuming perfectsynchronisation, the received signal impinging at receive antenna ν atsampling instants t=[n+lN_(sym)]T_(spl) is obtained

$\begin{matrix}{y_{l,n}^{(v)}\overset{\bigtriangleup}{=}{y^{(v)}\left( {\left\lbrack {n + {l\; N_{sym}}} \right\rbrack T_{spl}} \right)}} \\{\mspace{34mu}{= \left. {{\sum\limits_{\mu = 1}^{N_{T}}{\int_{- \infty}^{\infty}{{{h^{({\mu,v})}\left( {t,\tau} \right)} \cdot {x^{(\mu)}\left( {t - \tau} \right)}}\mspace{11mu}{\mathbb{d}\tau}}}} + {n(t)}} \right|_{t = {{\lbrack{n + {l\; N_{sym}}}\rbrack}T_{spl}}}}}\end{matrix}$where n(t) represents additive white Gaussian noise, andNsym=N_(FFT)+N_(GI) accounts for the number of samples per OFDM symbol.The signal y_(l,n) received by the receiver is first serial to parallel(S/P) converted by a S/P converter 709 and the guard interval is removedby a GI block 711. The information is recovered by performing a discreteFourier transform (DFT) on the received block of signal samples (in FIG.4 a FFT transformer 713 is used) to obtain the output of the OFDMdemodulation Y_(l,I) in the frequency domain. The received signal atreceive antenna ν after OFDM demodulation is given by

$Y_{l,i}^{(v)} = {{\sum\limits_{\mu = 1}^{N_{T}}{X_{l,i}^{(\mu)} \cdot H_{l,i}^{({\mu,v})}}} + N_{l,i}}$where

X_(l, i)^((μ))and

H_(l, i)^((μ, v))denotes the transmitted information symbol and the channel transferfunction (CTF) of transmit antenna μ, at sub-carrier i of the l^(th)OFDM symbol, respectively. The term N_(l,i) accounts for additive whiteGaussian noise (AWGN) with zero mean and variance N_(o).

When transmitting an OFDM signal over a multi-path fading channel, thereceived signal will have unknown amplitude and phase variations. Forcoherent transmission, these amplitude and phase variations need to beestimated by a channel estimator.

In the following, reference is made to pilot symbol-aided channelestimation (PACE), where a sub-set of the transmitted data is reservedfor transmitting known information, termed “pilot symbols”. These pilotsare used as side information for channel estimation.

To formally describe the problem, the received pilot of OFDM symbollD_(t) at the (iD_(f))^(th) sub-carrier

$Y_{{\overset{\sim}{l}D_{t}},{\overset{\sim}{i}D_{f}}} = {{\sum\limits_{\mu = 1}^{N_{T}}{X_{{\overset{\sim}{l}D_{t}},{\overset{\sim}{i}D_{f}}}^{(\mu)}H_{{\overset{\sim}{l}D_{t}},{\overset{\sim}{i}D_{f}}}^{(\mu)}}} + {N_{{\overset{\sim}{l}D_{t}},{\overset{\sim}{i}D_{f}}}\mspace{34mu}\begin{matrix}{\overset{\sim}{l} = \left\{ {1,2,\mspace{11mu}\ldots\mspace{14mu},{L/D_{t}}} \right\}} \\{\overset{\sim}{i} = \left\{ {1,2,\mspace{14mu}\ldots\mspace{14mu},{N_{c}/D_{f}}} \right\}}\end{matrix}}}$where

$X_{{\overset{\sim}{l}D_{t}},{\overset{\sim}{i}D_{f}}}^{(\mu)}$and

$H_{{\overset{\sim}{l}D_{t}},{\overset{\sim}{i}D_{f}}}^{({\mu,v})}$denotes the transmitted pilot symbol and the channel transfer function(CTF) of transmit antenna μ, at sub-carrier i=ĩD_(f) of the l={tildeover (l)}D_(t) ^(th) OFDM symbol, respectively. It is assumed that theCTF varies in the l and in the i variable, i.e. in time and infrequency. The term N_({tilde over (l)}D) _(t) _(, ĩD) _(f) accounts foradditive white Gaussion noise. Furthermore, l represents the number ofOFDM symbols per frame, N_(c) is the number of sub-carriers per OFDMsymbol, D_(f) and D_(t) denote the pilot spacing in frequency and time,and N_(T) is the number of transmit antennas. The goal is to estimate

H_(l.i)^((μ))for all {l,i,μ} within the frame Y_(l,i) is measured. Additionally, thesymbols

X_(l.i)^((μ))at the location (l,i)=({tilde over (l)}D_(t), ĩD_(f)) are known at thereceiver. The channel estimation now includes several tasks:

-   1. The separation of N_(T) superimposed signals,-   2. Interpolation in case that D_(t) or D_(f) are larger than one,    and-   3. Averaging over the noise N_({tilde over (l)}D) _(t) _(, ĩD) _(f)    by means of exploiting the correlation of

$H_{{\overset{\sim}{l}D_{t}},{\overset{\sim}{i}D_{f}}}^{({\mu,v})}.$

In order to estimate

H_(l.i)^((μ))given Y_({tilde over (l)}D) _(t) _(, ĩD) _(f) , there are N_(c)equations with N_(c)N_(T) unknowns, when one OFDM symbol is considered.Thus, a straight-forward solution of this linear equation system does,in general, not exist. By transforming Y_({tilde over (l)}D) _(t)_(, ĩD) _(f) to the time domain, the number of unknowns can be reduced,making it possible to solve the resulting equation system in the timedomain. This approach has the advantage that DFT-based interpolation,which is a standard technique, can be combined with estimation andseparation of N_(T) superimposed signals in one step, resulting in acomputationally efficient estimator.

For time domain channel estimation for MIMO-OFDM systems, the receivedpilots of one OFDM symbol Y_({tilde over (l)}D) _(t) _(, ĩD) _(f) arepre-multiplied by the complex conjugate of the transmitted pilotsequence X*_({tilde over (l)}D) _(t) _(, ĩD) _(f) , for 1≦ĩ≦N′_(p). Thenthe result is transformed into the time domain via an N′_(p)-point IDFT.Subsequently, the N_(T) superimposed signals are separated by a matrixinversion. The time domain channel estimate is obtained by filtering theoutput of the IDFT operation with a finite impulse response (FIR)filter. The DFT-based interpolation is performed simply by addingN_(c)-Q zeros for the channel impulse response (CIR) estimates, i.e. toextend the length of the estimate of length Q to N_(c) samples. Thistechnique is called of zero padding. An N′_(p)-point DFT transforms theCIR estimate of the pilots to the frequency response estimate of theentire OFDM symbol.

Estimators based on discrete Fourier transform (DFT) have the advantagethat a computationally efficient transform in the form of the Fouriertransform does exist and that DFT based interpolation is simple.

The performance of the estimation in general is dependent on the choiceof the pilot symbols. It is desirable to chose a set of pilot sequences,which minimises the minimum mean squared error (MMSE) criterium (whichis a measure of the performance) and the computational complexity of theestimator. Estimators based on the least squares (LS) and the MMSEcriterion for OFDM-MIMO systems have been systematically derived by Y.Gong and K. Letaief in: “Low Rank Channel Estimation for Space-TimeCoded Wideband OFDM Systems,” in Proc. IEEE Vehicular TechnologyConference (VTC' 2001-Fall), Atlantic City, USA, pp. 722-776, 2001.

I. Barhumi et al describe in: “Optimal training sequences for channelestimation in MIMO OFDM systems immobile wireless channels”,International Zurich Seminar on Broadband Communications (IZS02),February, 2002 a channel estimation and tracking scheme for MIMO OFDMsystems based on pilot tones. In particular, the authors describe achannel estimation scheme based on pilot tones being orthogonal andphase-shifted to each other. Although the pilot symbols described in theabove-cited prior art allow an accurate channel estimation, an enormouscomputational complexity at the receiver is required in order to performmatrix inversions required by the channel estimation algorithm. Due tothis high computational complexity, the estimation scheme described inthe above prior art document cannot be implemented at low cost, so thatthe disclosed algorithm may not be suitable for mass-market mobilereceivers.

Yi Gong at al. (“Low Rank Channel Estimation for Space-Time CodedWideband OFDM systems”, IEEE Vehicular Technology Conference, VTC2001—Fall, vol. 2, pp. 772-776, September 2001) describe a channelestimation scheme with reduced complexity, wherein matrix inversions areavoided by applying pre-computed singular value decomposition in orderto estimate the channel. However, the complexity of this approach isenormous since the singular value decomposition has to be calculated.

Y. Li, et (“Simplified Channel Estimation for OFDM Systems with MultipleTransmit Antennas,” IEEE Transactions on Wireless Communications, vol.1, pp. 67-75, January 2002), proposed a channel estimation scheme forOFDM with multiple transmit antennas which is based on the DFTtransform. In particular, Li discloses a method for generating pilotsymbols to be transmitted by multiple transmit and receive antennas andto be exploited at the receiver for channel estimation. These pilotsymbols are generated by multiplying a training sequence having goodtiming and frequency synchronisation properties by a complex sequenceintroducing an additional phase shift between the pilot symbols andbetween the subsequent values of each pilot symbol, as well. To be morespecific, each value of a training sequence is multiplied by a complexfactor, which introduces a phase shift, wherein the phase shift isdependent of a number being assigned to the value being multiplied, on anumber assigned to the corresponding transmitting point and a totalnumber of transmitting points. The pilot symbols are orthogonal andphase shifted to each other. The pilot symbols are modulated by an OFDMscheme and transmitted through a plurality of communication channels. Ata receiver, which is one of a plurality of receivers, a signal beingreceived includes a super-position of the plurality of transmittedsignals through the plurality of communication channels. Li et alpresented further a design rule for the pilot tones based onphase-shifted sequences which is optimum in the mean squared error (MSE)sense. Moreover, a matrix inversion, which is, in general, required forthe estimator, can be avoided by choosing orthogonal pilot sequences.However, due to a difficulty of obtaining perfect orthogonality betweentraining sequences, matrix inversions may be necessary. Additionally, ifthe training sequences are non-orthogonal, then the channel estimationscheme proposed by Li becomes more complex since the paths correspondingto the communication channels cannot be separated in straight forwardway.

FIG. 5 shows prior art channel estimation scheme as taught by Li, wherethe case of two transmitting antennas is considered.

The prior art channel estimator includes a plurality of multipliers,wherein FIG. 5 shows only three multipliers being associated with thek^(th) value of a n^(th) received sequence r[n,k]. A first multiplier901, a second multiplier 903 and a third multiplier 905 arranged inparallel include first and second inputs and outputs, respectively. Theoutput of the first multiplier 901 is connected to a first inverse fastFourier transform (IFFT) block 907, the output of the second multiplier903 is connected to a second IFFT block 909 and the output of the thirdmultiplier 905 is connected to the third IFFT block 911. It should bementioned here that in total, K multipliers are connected to each IFFTblock, wherein K denotes a length of a received sequence in thefrequency domain, and a total number of 3K input signals are provided tothe three IFFT blocks. Each of the IFFT blocks 907, 909 and 911 isoperative to perform an inverse fast Fourier algorithm applied to Kinput values, respectively. Furthermore, each of the IFFT blocks 907,909 and 911 includes a number of outputs, wherein only the first K₀outputs of each IFFT block are used. The respective remaining outputsare, for example, connected to ground.

K₀ outputs of the first IFFT block 907 are connected to a firstestimation block 913 and the first K₀ outputs of the third IFFT block911 are connected to a second estimation block 915. The K₀ outputs ofthe second IFFT block 909 are connected to the first estimation block913 and to the second estimation block 915, respectively. The firstestimation block 913 and the second estimation block 915 have K₀outputs, each of the outputs being connected to a corresponding filter917 of a plurality of filters, each of the filters having an output,respectively. The K₀ outputs of the filters 917 corresponding to thefirst estimation block 913 are connected to a first Fourier transform(FFT) block 917 and the K₀ outputs of the filter 917 corresponding tothe second estimation block 915 are connected to a second FFT block 921.The first FFT block 919 and the second FFT block 921 have K outputs,where K is, as stated above, the number of sub-carriers. Furthermore,due to the simplified algorithm described by Li, the outputs of thefirst filters 917 corresponding to the first estimation block 913 areconnected to the second estimation block 915 and the outputs of thefilter 917 corresponding to the second estimation block 915 are furtherconnected to the first estimation block 913, so that a plurality offeedback loops is established.

As stated above, FIG. 5 shows an example of the prior art estimator forthe case of two transmit antennas, so that the received signal r[n,k] isa superposition of two transmitted signals being possibly corrupted bychannel noise. The received signal is split into two received signals bya splitting means not shown in FIG. 5. The copies of the receivedsignals are then multiplied by complex conjugated signals correspondingto the respective transmit antennas. Moreover, the pilot symboltransmitted by the first transmit antenna is multiplied by a complexconjugated version of the pilot symbol transmitted by the secondantenna. More precisely, the K values of the first copy of the receivedsignal are multiplied by K values of the complex conjugated version ofthe pilot symbol transmitted by the first antenna. The K values of thesecond version of the received signal is multiplied by K values of thecomplex conjugated version of the pilot symbol transmitted by the secondtransmit antenna. Furthermore, the K values of the pilot symboltransmitted by the first antenna is multiplied by K complex conjugatedvalues of the pilot symbol transmitted by the second transmit antenna inorder to obtain intermediate values required by the subsequent channelestimation algorithm.

As stated above, all multiplications are performed in parallel, so thatthe K results from the multipliers 901 are fed to the first IFFT block907. K results from the K multipliers 903 are fed to the second IFFTblock 909. K results from the K multipliers 905 are fed to the thirdIFFT block 911. Each respective IFFT block is operative to perform aninverse fast Fourier transform in order to transform the frequencydomain input signals into time domain output signals.

The first and the second estimation block, 913 and 915, are operative toperform a channel estimation algorithm based on the plurality of theinput signals. More precisely, the first estimation block 913 receives3K₀ input signals to generate K₀ output signals corresponding to thechannel impulse response of the first channel from the first transmitantenna to the considered receive antenna. The second estimation block915 receives, in an analogue way, 3K₀ input signals to generate K₀output values corresponding to the second communication channel from thesecond transmit antenna to the receive antenna. The respective K₀ outputvalues are then filtered by filters 917.

As stated above, the respective output signals from the filters are fedback to the first and second channel estimation blocks 913 and 915,since the channel estimation blocks 913 and 915 are operative toestimate the channel impulse response of the respective communicationchannels based on previously-calculated values and on current valuesobtained from the IFFT blocks. Each estimation block applies anestimation algorithm where matrix by vector multiplications instead ofmatrix inversions are performed in order to calculate desired channelimpulse responses. After filtering and zero padding to a length requiredby the following fast Fourier transform, a channel transfer function ofthe first and of the second communication channels are obtained.

As stated above, Li avoids matrix inversions by introducing an iterativescheme where matrix by vector multiplications appear and by exploitingthe orthogonality of the pilot symbols. However, in order to calculatetwo channel impulse responses corresponding to the two communicationchannels, three inverse fast Fourier transforms and 3K multipliers arerequired. Moreover, the channel estimation algorithm applied by Li hasstill a high complexity due to the required matrix by vectormultiplications. Hence, with an increasing number of transmit antennas,the complexity of the complicated estimation scheme proposed by Lirapidly increases due to the high number of complex valuedmultiplications. In addition, the multiplication of the two pilotsymbols followed by an inverse Fourier transform is necessary in orderto provide a plurality of intermediate values required for channelestimation. Hence, the estimation blocks 913 and 915 cannot operateindependently, so that additional timing and control operations arenecessary.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an improved conceptfor channel estimation with reduced complexity.

In accordance with a first aspect, the present invention provides anapparatus for estimating a channel from a transmitting point to areceiving point in an environment, in which at least two transmittingpoints spaced apart from each other are present, each transmitting pointhaving associated therewith a pilot sequence, wherein the pilotsequences are different from each other, having: a provider forproviding an input signal, the input signal including a superposition ofsignals from the transmitting points; a multiplier for providing anumber of copies of the input signal, the number of copies being equalto the number of transmitting points; for each copy of the input signal,a transformer for transforming the copy or a signal derived from thecopy to obtain a transformed signal, the transformer being operative toapply a transform algorithm, which is based on a Fourier transform; andfor each transformed signal, an extractor extracting a portion of thetransformed signal to obtain an estimated channel impulse response forthe channel to be estimated, wherein each extractor is operative toreceive a transformed signal only from an associated transformer.

In accordance with a second aspect, the present invention provides anapparatus for estimating a channel from a transmitting point to areceiving point in an environment, in which at least two transmittingpoints spaced apart from each other are present, each transmitting pointhaving associated therewith a pilot sequence, wherein the pilotsequences are different from each other, having: a provider forproviding an input signal, the input signal including a superposition ofsignals from the transmitting points; a transformer for transforming theinput signal or a copy of the input signal to obtain a transformedsignal, the transformer being operative to apply a transform algorithm,which is based on a Fourier transform; a multiplier for providing anumber of copies of the transformed signal, the number of copies beingequal to the number of transmitting points; for each copy of thetransformed signal, an extractor extracting a portion of the copy of thetransformed signal to obtain an estimated channel impulse response forthe channel to be estimated.

In accordance with a third aspect, the present invention provides amethod for estimating a channel from a transmitting point to a receivingpoint in an environment, in which at least two transmitting pointsspaced apart from each other are present, each transmitting point havingassociated therewith a pilot sequence, wherein the pilot sequences aredifferent from each other, having the following steps: providing aninput signal, the input signal including a superposition of signals fromtransmitting points; providing a number of copies of the input signal,the number of copies being equal to the number of transmitting points;for each copy of the input signal, transforming the copy or a signalderived from the copy to obtain a transformed signal by applying atransform algorithm, which is based on a Fourier transform; and for eachtransformed signal, extracting a portion of the transformed signal toobtain an estimated channel impulse response for the channel to beestimated, wherein only an associated transformed signal is received.

In accordance with a fourth aspect, the present invention provides amethod for estimating a channel from a transmitting point to a receivingpoint in an environment, in which at least two transmitting pointsspaced apart from each other are present, each transmitting point havingassociated therewith a pilot sequence, wherein the pilot sequences aredifferent from each other, having the following steps: providing aninput signal, the input signal including a superposition of signals fromtransmitting points; transforming the input signal or a signal derivedfrom the input signal to obtain a transformed signal by applying atransform algorithm, which is based on a Fourier transform; providing anumber of copies of the transformed signal, the number of copies beingequal to the number of transmitting points; and for each copy of thetransformed signal, extracting a portion of the copy transformed signalto obtain an estimated channel impulse response for the channel to beestimated.

In accordance with a fifth aspect, the present invention provides acomputer program having a program code for performing the method forestimating a channel from a transmitting point to a receiving point inan environment, in which at least two transmitting points spaced apartfrom each other are present, each transmitting point having associatedtherewith a pilot sequence, wherein the pilot sequences are differentfrom each other, having the following steps: providing an input signal,the input signal including a superposition of signals from transmittingpoints; providing a number of copies of the input signal, the number ofcopies being equal to the number of transmitting points; for each copyof the input signal, transforming the copy or a signal derived from thecopy to obtain a transformed signal by applying a transform algorithm,which is based on a Fourier transform; and for each transformed signal,extracting a portion of the transformed signal to obtain an estimatedchannel impulse response for the channel to be estimated, wherein onlyan associated transformed signal is received, or the method forestimating a channel from a transmitting point to a receiving point inan environment, in which at least two transmitting points spaced apartfrom each other are present, each transmitting point having associatedtherewith a pilot sequence, wherein the pilot sequences are differentfrom each other, having the following steps: providing an input signal,the input signal including a super-position of signals from transmittingpoints; transforming the input signal or a signal derived from the inputsignal to obtain a transformed signal by applying a transform algorithm,which is based on a Fourier transform; providing a number of copies ofthe transformed signal, the number of copies being equal to the numberof transmitting points; and for each copy of the transformed signal,extracting a portion of the copy transformed signal to obtain anestimated channel impulse response for the channel to be estimated, whenthe program runs on a computer.

The present invention is based on the finding that a channel estimationscheme based on Fourier transform can be simplified by efficientlyexploiting the properties of the Fourier transform. In particular, ithas been found that a transform based on a Fourier transform, forexample a Fourier transform or an inverse Fourier transform, provides anestimated channel impulse response of a communication channel extendingfrom a transmitting point of a plurality of transmitting points to areceiving point, if the transmitting points transmit different pilotsequences for channel estimation at the receiving point. In particular,if the pilot sequences are orthogonal and phase shifted to each other,then a transform based on a Fourier transform directly provides anestimated channel response of a channel to be estimated.

For example, in an environment, in which at least two transmittingpoints transmit pilot sequences for channel estimation, a signalreceived at the receiving point includes a superposition of the signalstransmitted by the respective transmitting points, wherein the signalreceived at the receiving point may be both: a time domain signalbelonging to a single carrier modulation scheme or a frequency domainsignal belonging to a multicarrier modulation scheme, e.g. OFDM.

Since the pilot sequences are different from each other and thetransmitting points are spaced apart from each other in order to, forexample, exploit positive characteristics of a space diversitytransmission scheme, an input signal provided by a provider, which mayinclude an antenna, a filter applied to the signal received at thereceiving point etc., includes a superposition of signals from thetransmitting points, each of the signal being transmitted through arespective communication channel.

For the above considered case of two transmitting points transmittinginformation, the input signal includes a superposition of two signalstransmitted through two physical channels having possibly differentcharacteristics. If the input signal is multiplied in such a way that itis split or divided into two possibly identical copies, wherein ingeneral a number of copies is equal to a number of transmitting points,then each copy of the input signal includes an associated pilot sequenceinformation, i.e. the respective phase shift overlaid by a channelinformation associated with a channel the respective pilot sequence wastransmitted through.

Each copy of the input signal is then pre-multiplied by a signal derivedfrom a training sequence associated with a channel to be estimated.Hence, if each copy of the input signal is transformed by a transformerbased on a Fourier transform which efficiently exploits the phaseinformation of the particular pilot sequence, then a transformed signalprovided by the transformer applied to the copy of the input signalincludes a channel impulse response of the first channel, and thetransformer applied to a further copy of the input signal includes afurther channel impulse response of a further communication channel.

While the estimator disclosed by Li at al. requires a plurality ofadditional Fourier transforms in order to compute the intermediatevalues required for the channel estimation scheme, only one IDFToperation per communication channel is required in order to estimate thechannel impulse response which simplifies the receiver structure andreduces the complexity of the inventive channel estimation scheme.Moreover, the improvement of the proposed receiver structure compared tothe prior art receiver structure has no negative effects on theperformance of the channel estimator.

Furthermore, due to the inventive channel estimation scheme,significantly less multiplications have to be performed which leads to afurther complexity reduction since no pilot sequence by pilot sequencemultiplication have to be performed in order to obtain intermediateresults.

Additionally, the inventive channel estimation scheme is simplified incomparison with the prior art channel estimation schemes since thetransformed signal already contains an estimate of the channel impulseresponse to be estimated. Therefore, no matrix inversions or matrix byvector multiplications are necessary which further reduces thecomplexity of the receiver structure.

Moreover, the inventive channel estimation scheme can be applied to anyof orthogonal sequences having different phase shifts to each otherprovided that these phase shifts are known at the receiving point, sincethe respective transformer for providing a particular channel's estimatecan efficiently be adjusted to the phase shift of the pilot sequencetransmitted through the channel to be estimated.

The inventive approach can further be applied to channel estimation inany transmission systems, i.e. in multiple access transmission systems,like frequency division multiple access or time division multiple accesssystems.

BRIEF DESCRIPTION OF THE DRAWINGS

Further embodiments of the present invention are described in detailwith respect to the following figures, in which:

FIG. 1 shows a block diagram of an inventive apparatus for estimating achannel in accordance with a first embodiment of the present invention.

FIG. 2 shows a block diagram of a further apparatus for estimating achannel in accordance with a further embodiment of the presentinvention;

FIG. 3 shows a block diagram of an inventive apparatus for estimating achannel in accordance with a further embodiment of the presentinvention;

FIG. 4 demonstrates an OFDM modulation scheme; and

FIG. 5 shows a block diagram of a prior art channel estimation scheme.

FIG. 6 shows a block diagram of an inventive apparatus for estimating achannel in accordance with a further embodiment of the presentinvention.

DESCRIPTION OF PREFERRED EMBODIMENTS

In FIG. 1 a block diagram of an inventive apparatus for estimating achannel is shown, wherein the apparatus is embedded in a multiple outputscenario characterized by a plurality of transmit antennas. For the sakeof clarity FIG. 1 shows only two transmit antennas, 101 and 103.

The apparatus shown in FIG. 1 comprises a receive antenna 105 having anoutput connected to a provider 107. The provider 107 has an outputconnected to a multiplier 109 for providing a number of copies of theinput signal. The multiplier 109 has a number of outputs, the numbercorresponding to a number of copies to be provided or, in other words,corresponding to a number of transmitting points. For the sake ofsimplicity, only an output 111 and a further output 113 of themultiplier 109 are depicted in FIG. 1.

The output 111 is connected to a transformer 115, and the further output113 is connected to a transformer 117. Each of the transformers 115 and117 has a number of outputs corresponding to a transform performed bythe respective transformer or, more precisely, corresponding to atransform length. The number of outputs of the transformer 115 isconnected to an extractor 119, and the number of outputs of thetransformer 117 is connected to an extractor 121. The extractor 119 andthe extractor 121 have a number of outputs, wherein the number ofoutputs of the respective extractor 119 or 121 is equal to or preferablysmaller than the number of outputs of the respective transformer 115 and117.

The receive antenna 105 receives analogue signals from the plurality oftransmitting points. Hence, the input signal includes a superposition ofsignals from the plurality of transmitting points. The provider 107performs for example a filtering, analogue-to-digital conversion,demodulation or the like, so that the input signal provided at theoutput 108 of the provider 107 is a discrete time or frequency domainsignal depending on the underlying demodulation scheme. For example, ifan OFCM modulation scheme is used, then the input signal provided at theoutput 108 is a frequency domain signal. On the contrary, if a singlecarrier modulation scheme is used, then the input signal provided at theoutput 108 is a time domain signal.

The multiplier 109 receives the input signal via the output 108 andprovides a number of copies of the input signal, wherein the number ofcopies is equal to the number of transmitting points as described above.The multiplier 109 may for example be operative to generate the numberof exact copies of the input signal and to provide the number of pathscorresponding to the number of transmitting points, wherein each path isassociated with one copy of the input signal.

Preferably, for each copy of the input signal, a transformer fortransforming the copy or for transforming a signal derived from the copyis applied. In FIG. 1 the copy provided at the output 111 is onlyreceived by the transformer 115, and the copy of the input signalprovided via the output 113 (further copy) is only received by thetransformer 117. In other words, the transformer 115 is assigned only tothe copy of the input signal provided by the output 111 and thetransformer 117 is assigned only to the further copy of the input signalprovided by the output 113. Moreover, as depicted in FIG. 1, thetransformers 115 and 117 operate independently from each other.

The transformer 115 provides via the number of outputs a transformedsignal corresponding to a communication path between a transmittingpoint and the receiving point, and the transformer 117 provides via thenumber of outputs a transformed signal corresponding to a furthercommunication path between a further transmitting point and thereceiving point. Hence, the transformer 115 applies a transformalgorithm which is based on a Fourier transform to the copy of the inputsignal or to a signal derived from the copy of the input signal (by forexample a pre-multiplication) and the transformer 117 applies atransform algorithm based on the Fourier transform the further copy ofthe input signal or to a signal derived from the further copy of theinput signal in order to obtain transformed signals.

The transformer 115 and the transformer 117 may be operative to performa Fourier transform, a discrete Fourier transform, a fast Fouriertransform, an inverse Fourier transform, an inverse discrete Fouriertransform or an inverse fast Fourier transform. In general, theplurality of transformers applied to transforming the signals providedby the multiplier are operative to perform a transform algorithmtransforming phase shifts of the particular training sequence such thata particular channel information may be retrieved. This can be performedby transforming phase shifts into delays, which is an inherent propertyof the algorithms based on Fourier transform.

The inventive channel estimation scheme is based on separate processingof each path corresponding to a respective copy of the input signal,wherein the number of paths corresponds to the number of transmittingpoints or to the number of communication channels to be estimated.Moreover, the inventive channel estimation scheme requires only onetransformer per communication channel to be estimated. In other words,if N_(T) transmitting points transmit pilot sequences for estimating ofN_(T) communication channels, then at most N_(T) transformers arenecessary for providing the channel estimates. Since the respectivetransformers may operate independently, the channel estimates areprovided without using any intermediate values. To be more specific, inorder to estimate a particular communication channel, only onetransformer and additionally only the knowledge of the pilot sequenceassociated wit the corresponding channel (channel impulse response) tobe estimated is required. In contrast to the prior art channelestimation scheme, neither cross connects between the transformers norintermediate results obtained from a combination of training sequencesare necessary.

For each transformed signal, an associated extractor extracting aportion of the transformed signal is applied to obtain an estimatedchannel impulse response for the channel to be estimated. In FIG. 1, theextractor 119 extracts a portion of the transformed signal provided bythe transformer 115, and the extractor 121 extracts a portion of thetransformed signal provided by the transformer 117. Extracting theportion of respective transformed signal means that only a subset ofdiscrete values provided by the respective transformer 115 and 117 isfurther used.

For example, the extractor 119 and 121 may be operative to extract anumber of successive values from the respective transformed signalprovided by the transformer 115 and 117, wherein the number ofsuccessive values can be determined from a pre-knowledge of the channel,for example from a pre-known channel length. In this case, the extractor119 extracts a subset from the corresponding transformed signal, thesubset being no longer than the channel length of the channel to beestimated. However, the pre-knowledge of the channel may be a channelenergy. In this case, the extractor 119 extracts a subset of thetransformed signal, such that the subset extracted from the transformedsignal has an energy which is greater than for example 80% of thechannel energy. The remaining discrete values of the respectivetransformed signal, which are not extracted, may be discarded by settingsame, for example, to zero. The extractor 121 operates in exactly thesame way.

Moreover, the extractors 119 and 121 may be operative to extract valuesfrom the respective transformed signal, wherein values are greater thana predetermined threshold. For example, the predetermined thresholddetermines a minimum magnitude of values to be extracted. Thepredetermined threshold may be obtained from a maximum magnitude valueincluded in the transformed signal. For example, the predeterminedthreshold may be equal to 0.2 of the maximum magnitude value.Furthermore, if an energy criterion is used for extracting a portion ofthe transformed signal, the predetermined threshold may be chosen suchthat the discrete values included in the transformed signal being abovethe threshold have energy no smaller for example than 80% of the channelenergy. Alternatively, the threshold may be chosen such that an energyof discarded values, i.e. values not to be extracted, is less than forexample 20% of the channel energy. In order to perform a thresholdoperation, the extractor may further comprise a comparator for comparingthe discrete values included in the respective transformed signal to thethreshold.

As depicted in FIG. 1, the portion of the transformed signal extractedby the extractor 119 is an estimated channel impulse of the channelextending for example from the transmitting point 101 to the receivingantenna 105. The portion of the transformed signal provided by theextractor 121 is the estimated channel impulse response of the furtherchannel extending for example from the transmit antenna 103 to thereceive antenna 105. Clearly, each extractor is operative to receive atransformed signal only from an associated transformer. To be morespecific, each extractor operates only on the transformed signalprovided by the associated transformer so that the respective channelimpulse estimate can separately be estimated especially when the pilotsequences used for channel estimation are orthogonal to each otherwithin a predetermined orthogonality range and phase shifted to eachother, so that the properties of Fourier transformed can efficiently beexploited. However, since a perfect orthogonality is difficult toachieve, it is allowable that an absolute value of an inner product ofany two pilot sequences is greater than or equal to zero but preferablysmaller than 0.2. Hence, the predetermined orthogonality range isdefined by an interval having a first value equal to zero and a lastvalue equal to 0.2.

In accordance with a further embodiment of the present invention, theoperations of multiplying and transforming may be interchanged. Thisembodiment is illustrated in FIG. 6. In this case, a transformer 116transforms the input signal or a copy of the input signal to obtain atransformed signal by using a transform algorithm, which is based on aFourier transform. Hereafter, a number a number of copies of thetransformed signal may be provided by a multiplier 110, wherein thenumber of copies is preferably equal to the number of transmittingpoints. For each copy of the transformed signal, an extractor 119, 121may be used for extracting a portion of the copy of the transformedsignal to obtain an estimated channel impulse response for the channelto be estimated.

FIG. 2 shows an inventive apparatus for estimating a channel 35 inaccordance with a further embodiment of the present invention, whereinagain case of two transmitting points, i.e. two communication channels,is considered.

In contrast to the apparatus shown in FIG. 1, the apparatus shown inFIG. 2 comprises a pre-multiplier 201 having an input connected to theoutput 111 of the multiplier 109 and an output 203 connected to thetransformer 115. Additionally, the pre-multiplier 201 has a furtherinput 202. Furthermore, the apparatus shown in FIG. 3 comprises apre-multiplier 207 having an input connected to the output 113 of themultiplier 109 and an output 209 connected to the transformer 117.Additionally, the pre-multiplier 207 has a further input 208.

In a further contrast to the embodiment shown in FIG. 1, the apparatusdisplayed in FIG. 2 includes a means 211 for processing connected to theoutputs of the extractor 119, wherein the means 211 for processing has anumber of outputs, the number of outputs being equal to or smaller thanthe number of outputs of the extractor 119. Additionally, the apparatuscomprises a means 213 for processing connected to the extractor 121,wherein the means 213 has a number of outputs being equal or smallerthan the number of outputs of the extractor 121. Clearly, the means 211for processing is associated with a communication path and the means 213for processing is associated with a further communication path.

In a further contrast to the apparatus shown in FIG. 1, thepre-multipliers 201 and 207 connected between the multiplier 109 and therespective transformer 115 and 117 are present. The path correspondingto the output 111 of the multiplier 109 provides a signal to beexploited for estimation of the communication channel, and the furtherpath associated with the output 113 of the multiplier 109 provides asignal to be exploited for estimation of the further communicationchannel.

In particular, the pre-multiplier 201 is operative to pre-multiply theinput signal, i.e. the copy thereof provided by the output 111, by acomplex conjugate version of a pilot sequence associated with thetransmitting point defining the channel to be estimated, wherein thecomplex conjugate version of the pilot sequence associated with thefirst transmitting point is provided to the multiplier 201 via thefurther input 202. However, in case that the pilot sequence is an allone sequence or if the coefficients of the pilot sequence vary onlywithin a small range (i.e. smaller than 0.1 of a ratio between a maximummagnitude and a minimum magnitude), the pre-multiplier 201 may bebypassed by the input signal provided by the output 111 to thetransformer 115.

However, since a plurality of different pilot sequences are transmitted,at least one pilot sequence has coefficients which are not all one.Hence, the pre-multiplier 207 pre-multiplies the input signal (thefurther copy thereof) provided via the output 113 by a complex conjugateversion of a further pilot sequence associated with the furthertransmitting point defining the further channel to be estimated.

It should be noted here that the versions of pilot sequences provided tothe respective pre-multiplier 201 and 207 must not necessarily becomplex conjugate since the conjugation can be accounted duringmultiplications performed by the respective pre-multiplier 201 and/or207. Moreover, instead of conjugating the respective pilot sequence, therespective copy of the input signal provided to the respectivepre-multiplier my be conjugated, too, by for example introducing anadditional conjugation means between the pre-multiplier 109 and therespective pre-multiplier 201 or 207. Moreover, the pre-multiplicationsmay also be performed by the respective transformer or by the multiplier109.

Moreover, foe example when the input signal belongs to an OFDMmodulation scheme using M-ary QAM (M being greater than 4), thepre-multiplier 201 and 207 my be operative to pre-multiply the inputsignal (or copies thereof) provided via the outputs of the multiplier109 by a version of an inverse of a pilot sequence associated with thechannel to be estimated, wherein the version may be equal to therespective inverse or equal to a complex-conjugate version thereof. Inthis case, the inventive apparatus may further comprise a processingmeans for performing the necessary inversions. Alternatively, thepre-multiplier may be configured to perform the necessary divisions.

The pre-multiplied signal provided by the pre-multiplier 201 is providedto the transformer 115, and the pre-multiplied signal provided by thepre-multiplier 207 is provided to the transformer 117. The transformers115 and 117 apply a single transform algorithm to the associatedpre-multiplied signal, so that the extractor 119 and the extractor 121are capable of extracting channel estimates from the respectivetransformed signals as described above.

In contrast to the apparatus displayed in FIG. 1, the apparatus shown inFIG. 2 further includes means for processing 211 and 213. The means forprocessing 211 is operative to provide an enhanced estimated channelimpulse response based on the estimated channel impulse responseprovided by the extractor 119, and the means 213 for processing isoperative to provide a further enhanced estimated channel impulseresponse based on the further estimated channel impulse responseprovided by the extractor 121. For example, the means 211 and 213 areoperative to reduce an estimation error included in the respectiveestimated channel impulse response due to for example a possible channelnoise.

It should be remarked that the means for processing as represented bythe means 211 and 213 operate on the portion extracted by the associatedextractor 119 and 121 without any knowledge of any further pilotsequence. The means 211 for processing may be operative only oninformation associated with the corresponding processing path, i.e. themeans 211 does not need any information of the further pilot sequenceassociated with the further processing path and vice versa.

Each of the means for processing may further comprise a channelestimator, for example a minimum mean square error (MMSE) estimator, aleast square (LS) estimator or a maximum likelihood (ML) estimator orfurther variations thereof. The respective means for processing anoperative to reduce the channel noise corrupting the received channelestimates by providing a better—enhanced—estimates. The means forprocessing may perform a filter operation, i.e. Wiener filtering,wherein the filter coefficients are obtained from a MMSE criterion.

Moreover, the means for processing may perform a simple thresholdoperation thresholding the respective estimate of the channel inputresponse so that coefficients of the respective channel estimate belowthe threshold are discarded or zeroed. For example, the threshold may bederived from an energy criterion similar to the one described above.Furthermore, the threshold operation may only be applied to a number oflast coefficients of each channel estimate provided by the respectiveextractor in order shorten the length of the respective channelestimate.

Moreover, the means for processing as represented by means 211 and 213may comprise an estimation filter as described above, wherein theestimation filter may iteratively be adjusted, and wherein the iterativeadjust scheme is based on the portions extracted from the correspondingextractor at different time instants for iteratively outputting enhancedestimated channel impulse responses. For example, the means forprocessing may be operative to determine the filter coefficientsiteratively on the basis of previously obtained enhanced channelestimates, so that current enhanced channel estimates may be provided.Moreover, the means for processing may be operative for channel trackingif the pilot sequences are only available at distinct time instants orif a number of successively transmitted pilot sequences from onetransmitting point is too small for sufficient channel estimation.

In order to more precisely describe pilot symbol-assisted channelestimation, in the following a subset of the received signal will bedefined containing only the pilots

$\left\{ {\overset{\sim}{Y}}_{\overset{\sim}{l},\overset{\sim}{i}}^{(\mu)} \right\} = \left\{ Y_{l,i}^{(\mu)} \right\}$with {i,l}εG sampled at D_(f) times lower rate ĩ=└i/D_(f)┘ in frequencydirection, and at D_(t) times lower rate {tilde over (l)}=└l/D_(t)┘ intime direction, respectively.

Considering the pilot sequence of OFDM symbol l={tilde over (l)}D_(t)from transmit antenna μ which can be expressed by a column size vectorof size N′_(p)

$\begin{matrix}{{\overset{\sim}{Y}}_{\overset{\sim}{l}}^{\prime} = {{\sum\limits_{\mu = 1}^{N_{T}}{{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(\mu)}}{\overset{\sim}{H}}_{\overset{\sim}{l}}^{\prime{(\mu)}}}} + {\overset{\sim}{N}}_{\overset{\sim}{l}}^{\prime}}} & & & & & {\in C^{N_{P}^{\prime} \times 1}} \\{= {{\sum\limits_{\mu = 1}^{N_{T}}{{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(\mu)}}\overset{\sim}{F}I_{N_{P \times Q}^{\prime}}{\overset{\sim}{h}}_{\overset{\sim}{l}}^{\prime{(\mu)}}}} + {\overset{\sim}{N}}_{\overset{\sim}{l}}^{\prime}}} & & & & & \end{matrix}$where the transmitted pilot sequence, the channel transfer function(CTS) and additive noise term are given by

$\begin{matrix}{{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(\mu)}} = {{{diag}\left( {{\overset{\sim}{X}}_{\overset{\sim}{l},1}^{(\mu)},\cdots\mspace{11mu},{\overset{\sim}{X}}_{\overset{\sim}{l},N_{P}^{\prime}}^{\prime\;{(\mu)}}} \right)} \in C^{N_{P}^{\prime} \times N_{P}^{\prime}}}} \\{{\overset{\sim}{H}}_{\overset{\sim}{l}}^{\prime\;{(\mu)}} = {\left\lbrack {{\overset{\sim}{H}}_{\overset{\sim}{l},1}^{(\mu)},\cdots\mspace{11mu},{\overset{\sim}{H}}_{\overset{\sim}{l},N_{P}^{\prime}}^{(\mu)}} \right\rbrack^{T} \in C^{N_{P}^{\prime} \times 1}}} \\{{\overset{\sim}{h}}_{\overset{\sim}{l}}^{\prime\;{(\mu)}} = {\left\lbrack {{\overset{\sim}{h}}_{\overset{\sim}{l},1}^{(\mu)},\cdots\mspace{11mu},{\overset{\sim}{h}}_{\overset{\sim}{l},\overset{.}{Q}}^{(\mu)}} \right\rbrack^{T} \in C^{Q \times 1}}} \\{{\overset{\sim}{N}}_{\overset{\sim}{l}}^{\prime\;} = {\left\lbrack {{\overset{\sim}{N}}_{\overset{\sim}{l},1},\cdots\mspace{11mu},{\overset{\sim}{N}}_{\overset{\sim}{l},N_{P}^{\prime}}} \right\rbrack^{T} \in C^{N_{P}^{\prime} \times 1}}}\end{matrix}.$

The N′_(p)×N′_(p) DFT-matrix {tilde over (F)} transforms the CIR intothe frequency domain, defined by{{tilde over (F)}} _(i+1,n+1) =e ^(−j2πnilN′) ^(p) ; 0≦i≦N′ _(p)−1,0≦n≦N′ _(p)−1

In case that Q<N′_(p), the last N′_(p)-Q of the DFT output need to beremoved, which can be formally performed by the matrix I_(N′) _(p)_(×Q)=[I_(Q×Q), 0_(N′) _(p) _(−Q×Q)]^(T) of dimension N′_(p)×Q, withentries equal to 1 at the main diagonal and 0 elsewhere. For Q=N′_(p),the matrix I_(N′) _(p) _(×N′) _(p) becomes an identity matrix. Inpractice, the DFT transformation can be efficiently generated using aN′_(p)-point FFT. In case that Q<N′_(p), the last N′_(p)-Q outputs areskipped.

Hence, the flowing equation follows{tilde over (Y)}′ _({tilde over (l)}) ={tilde over (X)}′_({tilde over (l)}) {tilde over (H)}′ _({tilde over (l)}) +Ñ′_({tilde over (l)}) ={tilde over (X)}′ _({tilde over (l)}) {tilde over(F)} _(N) _(T) {tilde over (h)}′ _({tilde over (l)}) +Ñ′_({tilde over (l)})where

$\begin{matrix}{{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime} = {\left\lbrack {{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime{(1)}},\cdots\mspace{11mu},{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(N_{T})}}} \right\rbrack \in C^{N_{P}^{\prime} \times N_{T}N_{P}^{\prime}}}} \\{{\overset{\sim}{H}}_{\overset{\sim}{l}}^{\prime} = {\left\lbrack {{\overset{\sim}{H}}_{\overset{\sim}{l}}^{\prime{(1)}},\cdots\mspace{11mu},{\overset{\sim}{H}}_{\overset{\sim}{l}}^{\prime{(N_{T})}}} \right\rbrack^{T} \in C^{N_{T}N_{P}^{\prime} \times 1}}} \\{{\overset{\sim}{h}}_{\overset{\sim}{l}}^{\prime} = {\left\lbrack {{\overset{\sim}{h}}_{\overset{\sim}{l}}^{\prime{(1)}},\cdots\mspace{11mu},{\overset{\sim}{h}}_{\overset{\sim}{l}}^{\prime{(N_{T})}}} \right\rbrack^{T} \in C^{N_{T}Q \times 1}}} \\{{\overset{\sim}{F}}_{N_{T}}^{\prime\;} = {{{diag}\left( {{\overset{\sim}{F}I_{N_{P}^{\prime} \times Q}},\cdots\mspace{11mu},{\overset{\sim}{F}I_{N_{P}^{\prime} \times Q}}} \right)} \in C^{N_{T}N_{P}^{\prime} \times N_{T}Q}}}\end{matrix}.$

For time domain channel estimation the transmitted pilot sequence {tildeover (X)}′_({tilde over (l)}) is pre-multiplied by {tilde over(Y)}′_({tilde over (l)}) and the result is transformed into time domainvia for example a N′_(p)-point IDFT. These operations can mathematicallybe expressed as

$\begin{matrix}{\xi_{\overset{\sim}{l}}\overset{\bigtriangleup}{=}{\frac{1}{N_{P}^{\prime}}\left( {{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime}{\overset{\sim}{F}}_{N_{T}}} \right)^{H}{\overset{\sim}{Y}}_{\overset{\sim}{l}}^{\prime}}} & & & & & {\in C^{N_{T}Q \times 1}} \\{= {\frac{1}{N_{P}^{\prime}}{\overset{\sim}{D}}_{\overset{\sim}{l}}^{\prime\; H}{\overset{\sim}{Y}}_{\overset{\sim}{l}}^{\prime}}} & & & & & \\{= {{\frac{1}{N_{P}^{\prime}}{\overset{\sim}{D}}_{\overset{\sim}{l}}^{\prime\; H}{\overset{\sim}{D}}_{\overset{\sim}{l}}^{\prime}{\overset{\sim}{h}}_{\overset{\sim}{l}}^{\prime}} + {\frac{1}{N_{P}^{\prime}}{\overset{\sim}{D}}_{\overset{\sim}{l}}^{\prime\; H}{\overset{\sim}{N}}_{\overset{\sim}{l}}^{\prime}}}} & & & & & \end{matrix}$where the definition {tilde over (D)}′_({tilde over (l)})={tilde over(X)}′_({tilde over (l)}){tilde over (F)}_(N) _(T) has been introduced.The pre-multiplication with 1/N′_(p){tilde over (F)}_(N) _(T) ^(H)represents N_(T) IDFT operations, one N′_(p)-point IDFT for each blockof {tilde over (F)}_(N) _(T) .

The time domain channel estimate is obtained by filteringξ_({tilde over (l)}) with the weighting matrix w, that is,ĥ′_({tilde over (l)})=wξ′_({tilde over (l)})where ĥ′_({tilde over (l)}) has the same structure as {tilde over(h)}′_({tilde over (l)}).

Based on the above definitions, reference is made to FIG. 3 showing aninventive apparatus for estimating a channel in accordance with afurther embodiment of the present invention.

In FIG. 3, a case is considered where a plurality of transmitting pointstransmit pilot sequences for estimation of a respective channel at thereceiving point. For the sake of clarity, in FIG. 3 only two paths ofN_(T) paths corresponding to N_(T) transmitting points and, hence,corresponding to N_(T) communication channels are shown.

The input signal is provided by a multiplier not shown in FIG. 3. Themultiplier has a plurality of outputs, wherein successive N_(p) outputsare connected to a respective pre-multiplier. In accordance with theembodiment shown in FIG. 3, the first N_(p) outputs corresponding to acommunication path are connected to a pre-multiplier 301, and the lastN_(p) outputs corresponding to a further communication path areconnected to a pre-multiplier 303. The pre-multiplier 301 has a furtherinput 305 and an output 307. The pre-multiplier 303 has a further input309 and an output 311.

Furthermore, the apparatus shown in FIG. 3 comprises N_(T) frequencydomain (FD) windows. In particular, a frequency domain window 313 isconnected to the output 307 of the pre-multiplier 301 and a frequencydomain window 315 is connected to the output 311 of the pre-multiplier303. Each of the frequency domain windows has an output, wherein theoutput of the frequency domain window 313 is connected to a transformer317, and the output of the frequency domain window 315 is connected to atransformer 319. The transformer 317 and the transformer 319 areoperative to perform a N_(p)-point inverse Fourier transform (IFFT).

Instead of applying an extractor for extracting a number of outputs asdiscussed in connection with FIG. 2, first Q successive outputs of thetransformer 317 are connected to the filter 321 and the remainingoutputs are discarded. Accordingly, first Q successive outputs of thetransformer 319 are connected to the filter 312 and the remainingoutputs are discarded. In other words, the respective extractor isreplaced by hardwiring the respective Q outputs to the filter 321 and tothe filter 323.

The zero padder 325 has N_(C) outputs connected to a FFT transformer 329being operative to perform a N_(C)-point fast Fourier transform (FFT).The zero padder 327 has accordingly N_(C) outputs connected to a FFTtransformer 331 being operative to perform a N_(C)-point FFT.

The FFT transformer 329 has N_(C) outputs connected to an inverse window333 having a number of outputs, and N_(C) outputs of the FFT transformer331 are connected to an inverse window 335 having a number of outputs.

As shown in FIG. 3, each copy of the input signal is provided to anassociated pre-multiplier. In particular, a copy of the input signal isprovided to the multiplier 301, which pre-multiplies the copy by asignal derivable from a training sequence associated with thetransmitting point defining a channel to be estimated.

Accordingly, a further copy of the input signal provided to thepre-multiplier 303, which is operative to pre-multiply the further copyof the input signal (consisting of N_(p) discrete values) by a furthertraining sequence associated with a further transmitting point defininga further channel to be estimated.

It should be noted here that each version of the corresponding pilotsequence may be a complex conjugate pilot sequence, as described above.The pre-multiplied signals generated by the pre-multiplier 301 and thepre-multiplier 309 are provided to the respective frequency domainwindow 313 and 315, each of the frequency windows being operative toperform a frequency windowing in order to reduce leakage effects due tothe subsequent IFFT operation. For example, the frequency domain window313 and 315 may formed for filtering the respective pre-multipliedsignals in order to adjust the signals to be transformed such thatleakage effects are reduced.

Subsequently, the IFFT transformers 317 and 319 independently perform anIFFT algorithm applied to the output signals provided by the frequencydomain window 313 and the frequency domain window 315, respectively.

As described above, the filter 321 and 323 may be operative to perform afiltering in order to provide an enhanced estimated channel impulseresponse from the estimated channel impulse response and a furtherenhanced estimated channel impulse response from the further estimatedchannel impulse response by for example reducing an estimation errorcorrupting the respective channels estimate. For example, the filter 321and 323 perform a MMSE, LS or ML estimation. Moreover, the filter 321and 323 may be operative to perform a threshold operation as describedabove.

It should be noted here that the output signals of the IFFT transformers317 and 319 can directly be applied to equalization of time domain orfrequency domain signals. When for example the apparatus shown in FIG. 3is applied to channel estimation in a single carrier transmissionsystem. In time domain, for example a distributed feedback equalizer canbe applied for equalization. Moreover, the channel estimate and theenhanced channel estimate contain channel state information which may beexploited for channel coding and channel decoding purposes.

In order to obtain a channel transform function corresponding to therespective estimated channel impulse response or to the respectiveenhanced estimated channel impulse response, a subsequent fast Fouriertransform is applied to the enhanced estimated channel impulse responseprovided by the filter 321 and a fast Fourier transform is applied tothe further enhanced estimated channel impulse response provided by thefilter 323. Both transforms are performed in order to transform theparticular enhanced channel estimate into frequency domain for obtaininga channel transfer function associated with the enhanced estimatedchannel impulse and for obtaining a further channel transfer functionassociated with the further enhanced estimated channel impulse.

Prior to performing the respective FFT each of the enhanced channelestimates is zero padded to a length required by the subsequent FFTperformed by the respective IFFT transformer 329 and 331. To be morespecific, the zero padder 325 extends a length of the enhanced estimatedchannel impulse response provided by the filter 323 such that an outputsignal provided by the zero padder 325 has a length equal to N_(C)required by the subsequent FFT transform. A length of the furtherenhanced estimated channel impulse response provided by the filter 323is extended in an analogue way, so that the zero padder 327 providesN_(C) discrete values to the FFT transformer 331.

After the FFT transform, an inverse windowing is performed by theinverse window 333 and the inverse window 335 in order to reduce theeffects (influence) caused by the frequency domain window 313 and by thefrequency domain window 315.

It should be further noted here that the filter 321, the zero padder325, the FFT transformer 329 and the inverse window 333 constitute ameans for processing associated with the processing path and the filter323, the zero padder 327, the FFT transformer 331 and the followinginverse window 335 constitute a means for processing associated with thefurther processing path.

As described above, the received pilot sequence is pre-multiplied byN_(T) pilot sequences, each sequence corresponding to a signaltransmitted by a certain transmit antenna, followed by thetransformation to the time domain via the IDFT. DFT based interpolationis performed simply by adding N_(C)-Q zeroes to the channel impulseresponse estimate, extending the length of ĥ′_({tilde over (l)}) to anumber samples by means of zero padding, that is

$\begin{matrix}{h_{\overset{\sim}{l}D_{t}}^{\prime{(\mu)}} = \left\lbrack {{\overset{\sim}{h}}_{\overset{\sim}{l},1}^{(\mu)},\cdots\mspace{11mu},{\overset{\sim}{h}}_{\overset{\sim}{l},Q}^{(\mu)},0,\cdots\mspace{11mu},0} \right\rbrack^{T}} & & & & & \\{= \left\lbrack {{\overset{\sim}{h}}_{\overset{\sim}{l}}^{{\prime{(\mu)}}T},0,\cdots\mspace{11mu},0} \right\rbrack^{T}} & & & & & {\in C^{N_{FFT} \times 1}}\end{matrix}$wherein h′_({tilde over (l)}D) _(t) ^((μ)) denotes a vector. By means offiltering the channel estimate may be improved in the time domain. AnN_(C)-point DFT transforms the channel impulse response estimate of thepilots to the frequency response estimate of the entire OFDM symbol asconsidered in FIG. 3.

Provided that the channel impulse response is time limited,ξ_({tilde over (l)}) is strictly time limited and FFT basedinterpolation is simply performed by zero padding. It should be notedhere that zero padding is required even for the case where the pilotspacing D_(f) is equal to one since the number of outputs per transmitantenna is reduced by a factor of N_(T).

The estimate of the channel transform function of an entire OFDM symbol(pilots and data) is obtained by a N_(C)-point FFT of the zero paddedchannel impulse estimateĤ′=F_(N) _(T) ĥ′ or Ĥ′^((μ))=Fĥ′^((μ))where F_(N) _(T) is a N_(T)N_(c)×N_(T)N_(c) block diagonal DFT matrixconsisting of N_(T) blocks of N_(c)− point DFT matrices F.

An efficient implementation of the DFT is the fast Fourier transformalgorithm. For optimum efficiency, the number of points to the FFTshould be a power of 2. In practical systems, however, N_(C) and N′_(p)may not always be a power of 2. Therefore, zero padding may be used toemploy a fast Fourier transform. At the output, a number of last pointsof the obtained channel transfer function may be skipped to retain thedesired estimate. By doing so, it should be noted here that thetransform in the time domain must be adjusted, too, since theinterpolation ratio should be 1/D_(f). The interpolation ratio definesthe pilot spacing in frequency D_(f), which is equal to the reciprocalof the ratio between the inverse DFT to the time domain and, the backtransformation to the frequency domain, which is 1/D_(f).

In the following, reference is made to the least square estimators.Provided that the inverse of D′_({tilde over (l)})^(H)D′_({tilde over (l)}) does exist, the least squares estimator isgiven by

$\begin{matrix}{{\hat{h}}_{{LS}_{\overset{\sim}{l}}}^{\prime} = {{N_{P}^{\prime}\left( {D_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}} \right)}^{- 1}\xi_{\overset{\sim}{l}}^{\prime}}} \\{= {\left( {D_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}} \right)^{- 1}D_{\overset{\sim}{l}}^{\prime\; H}{{\overset{\sim}{Y}}_{\overset{\sim}{l}}^{\prime}\;.}}}\end{matrix}$

Since the estimator depends on the transmitted signal, the pilotsequences should be properly chosen. The LS estimator exists ifD′_({tilde over (l)}) is full rank, unfortunately this is not always thecase. A necessary condition for the LS estimator to exist isN′_(p)≧N_(T)Q.

In practice, two times oversampling provides a good trade off betweenminimizing the system overhead due to pilots and optimizing theperformance. It is assumed that the guard interval is longer than themaximum delay of the channel.

In the following, reference is made to a Wiener filter. The Wienerfilter is an estimator, which minimizes the MMSE of the received pilots.It is therefore also termed the MMSE estimator, described by a finiteimpulse response (FIR) filter. In general, the Wiener filter depends onthe location of the desired symbol n. In order to generate the MMSEestimator, knowledge of the correlation matrices R′_(ξξ) and R′_(hξ) isrequired. The MMSE estimate for OFDM symbol is given by

$\begin{matrix}{{\hat{h}}_{\overset{\sim}{l}}^{\prime} = {{R_{h\;\xi}^{\prime}R_{\xi\xi}^{\prime - 1}\xi_{\overset{\sim}{l}}^{\prime}} = {{w^{\prime}\xi_{\overset{\sim}{l}}^{\prime}} = {\frac{1}{N_{P}^{\prime}}w^{\prime}D_{\overset{\sim}{l}}^{\prime\; H}{\overset{\sim}{Y}}_{\overset{\sim}{l}}^{\prime}}}}} & \; & \; & \; \\{w^{\prime} = {R_{h\;\xi}^{\prime}R_{\xi\xi}^{\prime - 1}}} & \; & \; & {\in C^{{QN}_{T} \times {QN}_{T}}}\end{matrix}$where the correlation matrices R′_(ξξ) and R′_(hξ) are defined by

$\begin{matrix}{R_{\xi\xi}^{\prime}\overset{\bigtriangleup}{=}{E\left\{ {\xi_{\overset{\sim}{l}}^{\prime}\xi_{\overset{\sim}{l}}^{\prime\; H}} \right\}}} & {\in C^{{QN}_{T} \times {QN}_{T}}} \\{= {\frac{1}{N_{P}^{''2}}D_{\overset{\sim}{l}}^{\prime\; H}\; R_{\overset{\sim}{y}\overset{\sim}{y}}^{\prime}D_{\overset{\sim}{l}}^{\prime}}} & \\{= {{\frac{1}{N_{P}^{\prime 2}}D_{\overset{\sim}{l}}^{\prime\; H}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime}R_{\overset{\sim}{H}\overset{\sim}{H}}^{\prime}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}} + {\frac{N_{0}}{N_{P}^{\prime\; 2}}D_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}}}} & \\{= {{\frac{1}{N_{P}^{\prime 2}}D_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}R_{\overset{\sim}{h}\overset{\sim}{h}}^{\prime}D_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}} + {\frac{N_{0}}{N_{P}^{\prime\; 2}}D_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}}}} & \end{matrix}$and

$R_{h\;\xi}^{\prime}\overset{\Delta}{=}{{{E\left\{ {h_{\overset{\sim}{l}D_{t}}^{\prime},\xi_{\overset{\sim}{l}}^{\prime\; H}} \right\}}\mspace{20mu} \in \mspace{11mu} C^{{QN}_{T} \times Q\; N_{T}}}\mspace{34mu} = {\frac{1}{N_{P}^{\prime}}R_{h\;\overset{\sim}{h}}^{\prime}D_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}}}$

The co-variance in the time domain R′_({tilde over (h)}{tilde over (h)})is related to the co-variance matrix in the frequency domainR′_({tilde over (H)}{tilde over (H)}) by

$R_{\overset{\sim}{h}\;\overset{\sim}{h}}^{\prime} = {F_{N_{T}}^{H}R_{\overset{\sim}{H}\;\overset{\sim}{H}}^{\prime}F_{N_{T}}}$

Provided that the signals impinging from different transmit antennas aremutually uncorrelated, the autocorrelation matrix defined by

$R_{\overset{\sim}{h}\;\overset{\sim}{h}}^{\prime} = {E\left\{ {{\overset{\sim}{h}}_{\overset{\sim}{l}}^{\prime}{\overset{\sim}{h}}_{\overset{\sim}{l}}^{\prime\mspace{11mu} H}} \right\}}$has a block diagram form

$R_{\overset{\sim}{h}\;\overset{\sim}{h}}^{\prime\mspace{11mu}} = {{{diag}\;\left( {R_{\overset{\sim}{h}\;\overset{\sim}{h}}^{\prime\mspace{11mu}{(1)}},\mspace{14mu}\ldots\mspace{14mu},\; R_{\overset{\sim}{h}\;\overset{\sim}{h}}^{\prime\mspace{14mu}{(N_{T})}}} \right)}\mspace{11mu} \in \mspace{11mu}{C^{N_{T}Q \times N_{T}Q}.}}$

Moreover, the following relation holds

$R_{\overset{\sim}{h}\;\overset{\sim}{h}}^{\prime\mspace{11mu}{(\mu)}} = {\begin{bmatrix}R_{\overset{\sim}{h}\;\overset{\sim}{h}}^{\prime\mspace{11mu}{(\mu)}} \\0\end{bmatrix}\mspace{14mu} \in \mspace{11mu} C^{N_{FFT} \times Q}}$and

${R_{h\overset{\sim}{h}}^{\prime} = {{diag}\left( {R_{\overset{\sim}{h}\overset{\sim}{h}}^{\prime\mspace{11mu}{(1)}},\mspace{14mu}\ldots\mspace{14mu},R_{h\;\overset{\sim}{h}}^{\prime\mspace{11mu}{(N_{T})}}} \right)}},$where 0 denotes an all zero matrix of an appropriate dimension. Again,the above equation is exactly true only for the sample spaced channel.

It should be noted that while the LS estimator requiresD′_({tilde over (l)}) to be full rank, while the MMSE estimator requiresinvertability of R_(ξξ) as seen above. For this to hold, however,D′_({tilde over (l)}) does not need to be full rank. Thus, the MMSEestimator can exist even if N′_(p)<N_(T)Q.

For the case that D′_({tilde over (l)}) is full rank, the inverse ofD′_({tilde over (l)}) ^(H)D′_({tilde over (l)}) does exist. Then theWiener filter can be simplified to

$w^{\prime} = {N_{P}^{\prime}{R_{h\;\overset{\sim}{h}}^{\prime} \cdot \left\lbrack {R_{\overset{\sim}{h}\;\overset{\sim}{h}}^{\prime} + {\left( {D_{\overset{\sim}{i}}^{\prime\; H}D_{\overset{\sim}{i}}^{\prime}} \right)^{- 1}N_{0}}} \right\rbrack^{- 1} \cdot {\left( {D_{\overset{\sim}{i}}^{\prime\; H}D_{\overset{\sim}{i}}^{\prime}} \right)^{- 1}.}}}$

Thus, the corresponding MMSE estimate becomes

$\begin{matrix}{{\hat{h}}_{\overset{\sim}{l}}^{\prime} = {N_{P}^{\prime}{R_{h\;\overset{\sim}{h}}^{\prime} \cdot \left\lbrack {R_{\overset{\sim}{h}\overset{\sim}{h}}^{\prime\mspace{11mu}} + {\left( {D_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}} \right)^{- 1}N_{0}}} \right\rbrack^{- 1} \cdot \left( {D_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}} \right)^{- 1} \cdot \xi_{\overset{\sim}{l}}^{\prime}}}} \\{= {R_{h\;\overset{\sim}{h}}^{\prime} \cdot \left\lbrack {R_{\overset{\sim}{h}\overset{\sim}{h}}^{\prime} + {\left( {D_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}} \right)^{- 1}N_{0}}} \right\rbrack^{- 1} \cdot {\hat{h}}_{{LS}_{\overset{\sim}{l}}}^{\prime}}}\end{matrix}.$

That means that the LS estimate serves as an input for the MMSEestimator. By replacing

$D_{\overset{\sim}{i}}^{\prime\; H}D_{\overset{\sim}{i}}^{\prime}$by its average in the second equality, the MMSE estimator can be madeindependent of the transmitted pilots obtained in D′_({tilde over (l)}).It can be observed that the separation of the N_(T) signals, which isperformed by the LS estimator, can be separated from the filteringtasks.

It is generally assumed that the channel taps as well as the fading ofdifferent transmit antennas are mutually uncorrelated. Then, for thesample spaced channel the autocorrelation matrix has the diagonal form

$R_{\overset{\sim}{h}\;\overset{\sim}{h}}^{\prime\mspace{11mu}} = {{diag}\;\left( {\sigma_{1}^{{(1)}^{2}},\mspace{14mu}\ldots\mspace{14mu},\;\sigma_{Q}^{{(1)}^{2}},\mspace{14mu}\ldots\mspace{14mu},\mspace{11mu}\sigma_{Q}^{{(N_{T})}^{2}}} \right)}$where

σ_(Q)^((1)²)denotes the average received signal power of channel tap Q of the firsttransmit antenna.

In the following, reference is made to optimum pilot sequences. The MMSEestimator is in general dependent on the choice of the pilot symbols.However, choosing appropriate pilot sequences, the estimator becomesindependent of the transmitted pilots. It is desirable to choose a setof pilot sequences, which minimizes the MMSE (i.e. the performance ofthe estimator) and the computational complexity of the estimator. Amajor computational burden of the estimator is the matrix inversion of

$D_{\overset{\sim}{i}}^{\prime\; H}D_{\overset{\sim}{i}}^{\prime}$required by prior art channel estimation schemes for both the LSestimator as well as the MMSE estimator. If

$D_{\overset{\sim}{i}}^{\prime\; H}D_{\overset{\sim}{i}}^{\prime}$can be diagonalized, a computational expensive matrix inversion can beavoided, that is

${D_{\overset{\sim}{i}}^{\prime\; H}D_{\overset{\sim}{i}}^{\prime}} = {{{\overset{\sim}{F}}_{N_{T}}^{H}{\overset{\sim}{X}}_{\overset{\sim}{i}}^{H}{\overset{\sim}{X}}_{\overset{\sim}{i}}^{\prime}F_{N_{T}}} = {{N_{P}^{\prime}I}\mspace{31mu} \in {I^{N_{T}Q \times N_{T}Q}.}}}$

In the following, a sufficient condition will be derived whichdiagonalizes

$D_{\overset{\sim}{i}}^{\prime\; H}D_{\overset{\sim}{i}}^{\prime}$and therefore satisfies the above equation.

In order to keep the receiver complexity to a minimum it is desirable todiagonalize

$D_{\overset{\sim}{i}}^{\prime\; H}{D_{\overset{\sim}{i}}^{\prime}.}$Then, the LS and MMSE estimators can be grossly simplified. A necessarycondition for the diagonalization is N′_(p)≧N_(T)Q. The matrix

$D_{\overset{\sim}{i}}^{\prime\; H}D_{\overset{\sim}{i}}^{\prime}$can be expressed as

${D_{\overset{\sim}{l}}^{\prime\; H}D_{\overset{\sim}{l}}^{\prime}} = \begin{bmatrix}{I_{N_{P}^{\prime} \times Q}^{T}{\overset{\sim}{F}}^{H}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(1)}^{H}}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(1)}}\overset{\sim}{F}I_{N_{P}^{\prime} \times Q}} & \ldots & {I_{N_{P}^{\prime} \times Q}^{T}{\overset{\sim}{F}}^{H}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(1)}^{H}}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(N_{T})}}\overset{\sim}{F}I_{N_{P}^{\prime} \times Q}} \\\vdots & ⋰ & \vdots \\{I_{N_{P}^{\prime} \times Q}^{T}{\overset{\sim}{F}}^{H}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(N_{T})}^{H}}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(1)}}\overset{\sim}{F}I_{N_{P}^{\prime} \times Q}} & \ldots & {I_{N_{P}^{\prime} \times Q}^{T}{\overset{\sim}{F}}^{H}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(N_{T})}^{H}}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(N_{T})}}\overset{\sim}{F}I_{N_{P}^{\prime} \times Q}}\end{bmatrix}$where the blocks

${\overset{\sim}{F}}^{H}{\overset{\sim}{X}}_{\overset{\sim}{i}}^{{\prime{(\mu)}}^{H}}{\overset{\sim}{X}}_{\overset{\sim}{i}}^{\prime{(m)}}\overset{\sim}{F}$are of the dimension Q×Q.

A necessary condition for a diagonality is given by

${D_{\overset{\sim}{l}}^{\prime\mspace{11mu}{(\mu)}^{H}}D_{\overset{\sim}{l}}^{\prime\;{(m)}}}\overset{\Delta}{=}{{I_{N_{P}^{\prime} \times Q}^{T}{\overset{\sim}{F}}^{H}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\mspace{11mu}{(\mu)}^{H}}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(m)}}\overset{\sim}{F}\; I_{N_{P}^{\prime} \times Q}}\mspace{124mu} = \left\{ {\begin{matrix}{{N_{P}^{\prime}I},} & {\mu = m} \\{0,} & {\mu \neq m}\end{matrix}.} \right.}$

The first part is true for any pilot sequence since

${{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\;{(\mu)}^{H}}{\overset{\sim}{X}}_{\overset{\sim}{l}}^{\prime\mspace{11mu}{(\mu)}}} = {{I\mspace{14mu}{and}\mspace{14mu} I_{N_{P}^{\prime} \times Q}^{T}{\overset{\sim}{F}}^{H}\overset{\sim}{F}I_{N_{P}^{\prime} \times Q}} = {N_{P}^{\prime}{I_{Q \times Q}.}}}$

In the following, a sufficient condition to satisfy the above equationis derived. It is useful to examine the components of the vectorξ_({tilde over (l)},n). Without loss of generality, it is assumed thatthe signal from antenna 1 is to be estimated. Then, the entry ofξ_({tilde over (l)},n) ⁽¹⁾ is in the form

${\xi_{\overset{\sim}{l},n}^{(1)} = {{\frac{1}{N_{P}^{\prime}}{\sum\limits_{\mu = 1}^{N_{T}}\;{\sum\limits_{\overset{\sim}{i} = 1}^{N_{P}^{\prime}}\;{{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{{(1)}*}{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{(\mu)}{\mathbb{e}}^{{j2\pi} \cdot {({\overset{\sim}{i} - 1})} \cdot {{({n - 1})}/N_{P}^{\prime}}}{\sum\limits_{q = 1}^{Q}\;{{\overset{\sim}{h}}_{\overset{\sim}{l},q}^{(\mu)}{\mathbb{e}}^{{- {j2\pi}} \cdot {({\overset{\sim}{i} - 1})} \cdot {{({q - 1})}/N_{P}^{\prime}}}}}}}}} + {\frac{1}{N_{P}^{\prime}}{\sum\limits_{i = 1}^{N_{P}^{\prime}}\;{{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{{(1)}*}{\overset{\sim}{N}}_{\overset{\sim}{l},\overset{\sim}{i}}{\mathbb{e}}^{{j2\pi} \cdot {({\overset{\sim}{i} - 1})} \cdot {{({n - 1})}/N_{P}^{\prime}}}}}}}},\mspace{31mu}{n = \left\{ {1,\ldots,Q} \right\}}$

Rearranging the terms of the above equation yields

$\xi_{\overset{\sim}{l},n}^{(1)} = {{{\frac{1}{N_{P}^{\prime}}{\sum\limits_{\mu = 1}^{N_{T}}\;{\sum\limits_{q = 1}^{Q}{{\overset{\sim}{\; h}}_{\overset{\sim}{l},q}^{(\mu)}{\sum\limits_{\overset{\sim}{i} = 1}^{N_{P}^{\prime}}\;{{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{{(l)}*}{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{(\mu)}{\mathbb{e}}^{{j2\pi} \cdot {({\overset{\sim}{i} - 1})} \cdot {{({n - q})}/N_{P}^{\prime}}}}}}}}} + {{\overset{\sim}{n}}_{\overset{\sim}{l},n}\mspace{14mu} n}} = \left\{ {1,\mspace{11mu}\ldots\mspace{14mu},Q} \right\}}$where ñ_({tilde over (l)},n) represents an average white Gaussian noise(AWGN) process, which is generated from Ñ_({tilde over (l)},ĩ) bypre-multiplication with

${\overset{\sim}{X}}_{\overset{\sim}{i},\overset{\sim}{i}}^{(1)}$followed by an IDFT. The terms within the innermost sum are basically anIDFT of

${\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{{(1)}*}{{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{(\mu)}.}$

Before investigating the Fourier transform properties of the transmittedpilot sequences further, a DFT of an arbitrary sequence is defined by

${F_{N}\left( x_{n} \right)}_{k}\overset{\Delta}{=}{{\sum\limits_{n = 1}^{N}\;{x_{n}{\mathbb{e}}^{{- {j2\pi}}\;{k \cdot {{({n - 1})}/N}}}\mspace{20mu} k}} = {\left\{ {0,\mspace{11mu}\ldots\mspace{14mu},{N - 1}} \right\}.}}$

Furthermore, the following series is defined

$\begin{matrix}{{f_{N}(k)}\overset{\Delta}{=}{\frac{1}{N}{\sum\limits_{\overset{\sim}{n} = 0}^{N - 1}\;{\mathbb{e}}^{{- {j2\pi}}\; n\;{k \cdot {/N}}}}}} \\{= {{\frac{\sin\left( {\pi\; k} \right)}{N\;{\sin\left( {\pi\;{k/N}} \right)}} \cdot {\mathbb{e}}^{{- {j\pi}}\;{k \cdot {{({N - 1})}/N}}}} = {{\delta_{k}\mspace{34mu}{for}\mspace{14mu} 1} \leq k < N}}}\end{matrix}$where δ_(k) denotes the unit impulse function, defined by

$\delta_{k}\overset{\Delta}{=}\left\{ \begin{matrix}{1;} & {k = 0} \\{0;} & {elsewhere}\end{matrix} \right.$where 1≦k<N_(T) is an arbitrary constant. Hence, the following isobtained

$\xi_{\overset{\sim}{l},n}^{(1)} = {{\frac{1}{N_{P}^{\prime}}{\sum\limits_{\mu = 1}^{N_{T}}\;{\sum\limits_{q = 1}^{Q}\;{{\overset{\sim}{h}}_{\overset{\sim}{l},q}^{(\mu)}{F_{N_{P}^{\prime}}\left( {{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{{(1)}*}{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{(\mu)}} \right)}_{q - n}}}}} + {\overset{\sim}{n}}_{\overset{\sim}{l},n}}$

It can be seen that a sufficient condition for the orthogonality ofξ_({tilde over (l)},n) ⁽¹⁾ is to choose a set of pilot sequences withthe following properties

${{F_{N_{P}^{\prime}}\left( {{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{{(1)}*}{\overset{\sim}{X}}_{\overset{\sim}{l,}\overset{\sim}{i}}^{(\mu)}} \right)}_{q - n} = {c\;\delta_{n - q - {k\; Q}}}},$where c>0 is an arbitrary constant. In this case, the followingsimplification is obtained

${\xi_{\overset{\sim}{l},n}^{(1)} = {{{\sum\limits_{q = 1}^{Q}\;{{\overset{\sim}{h}}_{\overset{\sim}{l},q}^{(1)}\delta_{n - q}}} + {\overset{\sim}{n\;}}_{\overset{\sim}{l},n}} = {{{\overset{\sim}{h}}_{\overset{\sim}{l},n}^{(1)} + {{\overset{\sim}{n}}_{\overset{\sim}{l},n}\mspace{20mu}{for}\mspace{14mu} n}} = \left\{ {1,\mspace{11mu}\ldots\mspace{14mu},Q} \right\}}}},{Q \leq {N_{P}^{\prime}/{N_{T}.}}}$

Note that this condition is equivalent to diagonalizing

$D_{\overset{\sim}{i}}^{\prime\; H}{D_{\overset{\sim}{i}}^{\prime}.}$

By examining the DFT properties of orthogonal sequences such as Hadamardsequences, it can be shown that the above equation also is satisfied.Furthermore, the set of phase shifted sequences

${{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{(\mu)} = {\mathbb{e}}^{{- {j2\pi}} \cdot {({\overset{\sim}{i} - 1})} \cdot {{({\mu - 1})}/N_{T}}}};\mspace{25mu}{\mu = \left\{ {1,\mspace{14mu}\ldots\mspace{20mu},N_{P}^{\prime}} \right\}}$also satisfies the above equation, as will be shown in the following.These phase-shifted sequences may also be utilized to further simplifythe receiver structure. The DFT of

${\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{{(I)}^{*}}{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{(\mu)}$is given by

${F_{N_{P}^{\prime}}\left( {{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{{(I)}^{*}}{\overset{\sim}{X}}_{\overset{\sim}{l},\overset{\sim}{i}}^{(\mu)}} \right)}_{q - n} = {{N_{P}^{\prime}{f_{N_{P}^{\prime}}\left( {n - q - {\left( {\mu - 1} \right){N_{P}^{\prime}/N_{T}}}} \right)}} = {N_{P}^{\prime}{\delta_{n - q - {{({\mu - 1})}{N_{P}^{\prime}/N_{T}}}}.}}}$

Hence, the desired result for

$\xi_{\overset{\sim}{i,}n}^{(1)}$is obtained

$\begin{matrix}{\xi_{\overset{\sim}{l},n}^{(1)} = {{\sum\limits_{\mu = 1}^{N_{T}}\;{\sum\limits_{q = 1}^{Q}\;{{\overset{\sim}{h}}_{\overset{\sim}{l},q}^{(\mu)}\delta_{n - q - {{({\mu - 1})}{N_{P}^{\prime}/N_{T}}}}}}} + {\overset{\sim}{n}}_{\overset{\sim}{l},n}}} \\{{= {{{\overset{\sim}{h}}_{\overset{\sim}{l},n}^{(1)} + {{\overset{\sim}{n}}_{\overset{\sim}{l},n}\mspace{194mu}{for}\mspace{14mu} n}} = \left\{ {1,\mspace{11mu}\cdots\mspace{14mu},Q} \right\}}},{Q \leq {N_{P}^{\prime}/{N_{T}.}}}}\end{matrix}$

Therefore, if the pilot sequences are appropriately chosen, the LSestimator as well as the MSE estimator can grossly be simplified

$\begin{matrix}{w^{\prime} = {R_{h\;\overset{\sim}{h}}^{\prime} \cdot \left\lbrack {R_{\overset{\sim}{h}\;\overset{\sim}{h}}^{\prime} + {I\frac{N_{0}}{N_{P}^{\prime}}}} \right\rbrack^{- 1}}} \\{{\hat{h}}_{\overset{\sim}{l}}^{\prime} = {w^{\prime} \cdot \xi_{\overset{\sim}{l}}^{\prime}}} \\{{\hat{h}}_{{LS}_{\overset{\sim}{l}}}^{\prime} = {\xi_{\overset{\sim}{l}}^{\prime}.}}\end{matrix}$

It can be seen that the estimator has become independent of the chosenpilot sequence, which significantly simplifies the filter generation.

In the special case of a sample spaced channel, the Wiener filterbecomes

$w^{\prime} = {{{diag}\left( {\frac{\sigma_{1}^{{(1)}^{2}}}{\sigma_{1}^{{(1)}^{2}} + \frac{N_{0}}{N_{P}^{\prime}}},\mspace{11mu}\cdots\mspace{14mu},\frac{\sigma_{Q}^{{(1)}^{2}}}{\sigma_{Q}^{{(1)}^{2}} + \frac{N_{0}}{N_{P}^{\prime}}},\mspace{11mu}\cdots\mspace{14mu},\frac{\sigma_{Q}^{{(N_{T})}^{2}}}{\sigma_{Q}^{{(N_{T})}^{2}} + \frac{N_{0}}{N_{P}^{\prime}}}} \right)}.}$

For the non-sample spaced channel, the optimum solution for the Wienerfilter is not a diagonal matrix. However, most often a sub-optimumone-tap filter may be chosen.

Moreover, depending on certain implementation requirements of theinventive methods for estimating a channel can be implemented inhardware or in software. The implementation can be performed using adigital storage medium, in particular a disc or a CD havingelectronically readable control signals stored thereon, which cancooperate with a programmable computer system such that the inventivemethods are performed. Generally, the present invention is, therefore, acomputer-program product with a program code stored on amachine-readable carrier, the program code being for performing theinventive methods, when the computer program product runs on a computer.In other words, the inventive method is, therefore, a computer programhaving a program code for performing the inventive methods, when thecomputer program runs on a computer.

While this invention has been described in terms of several preferredembodiments, there are alterations, permutations, and equivalents whichfall within the scope of this invention. It should also be noted thatthere are many alternative ways of implementing the methods andcompositions of the present invention. It is therefore intended that thefollowing appended claims be interpreted as including all suchalterations, permutations, and equivalents as fall within the truespirit and scope of the present invention.

1. An apparatus for estimating a channel from a transmitting point to a receiving point in an environment, in which at least two transmitting points spaced apart from each other are present, each transmitting point having associated therewith a pilot sequence, wherein the pilot sequences are different from each other, comprising: a provider for providing an input signal, the input signal including a superposition of signals from the transmitting points; a multiplier for providing a number of copies of the input signal, the number of copies being equal to the number of transmitting points; for each copy of the input signal, a transformer for transforming the copy or a signal derived from the copy to obtain a transformed signal, the transformer being operative to apply a transform algorithm, which is based on a Fourier transform; and for each transformed signal, an extractor for extracting a portion of the transformed signal, the portion of the transformed signal representing an estimated channel impulse response for the channel to be estimated, wherein each extractor is operative to receive a transformed signal only from an associated transformer.
 2. The apparatus according to claim 1, wherein the pilot sequences are orthogonal to each other within a predetermined orthogonality range and phase shifted with respect to each other, the apparatus further comprising: for each extractor, a unit for processing the portion of the transformed signal extracted by an associated extractor without any knowledge of any pilot sequence.
 3. The apparatus according to claim 2, wherein the unit for processing comprises an estimation filter, the estimation filter being iteratively adjusted based on portions of the transformed signal extracted from the associated extractor at different time instants, the estimation filter being operative to output an enhanced estimated channel impulse response.
 4. The apparatus according to claim 3, wherein the unit for processing comprises a zero padder for zero padding the enhanced estimated channel impulse response to the predetermined length to obtain a zero padded enhanced estimated channel impulse response.
 5. The apparatus according to claim 4, wherein the unit for processing further comprises a transformer for transforming the zero padded enhanced estimated channel impulse response to output a channel transfer function of the channel to be estimated.
 6. The apparatus according to claim 5, wherein the apparatus further comprises a frequency domain window for windowing each signal derived from the copy to reduce the leakage effect and providing the resultant signal to a corresponding transformer, and wherein the apparatus further comprises an inverse window for windowing an output of the corresponding transformer to reduce an influence of the frequency domain window in the channel transform function of the channel to be estimated.
 7. The apparatus according to claim 1, further comprising, for each copy of the transformed signal, a pre-multiplier that is connected between the multiplier and each transformer to generate the signal derived from the copy, the pre-multiplier being operative to pre-multiply the corresponding of the input signal by a complex conjugate version of a pilot sequence associated with a transmitting point defining the channel to be estimated to obtain a pre-multiplied input signal.
 8. The apparatus according to claim 1, wherein the extractor is operative to extract values from the transformed signal being greater than a pre-determined threshold.
 9. An apparatus for estimating a channel from a transmitting point to a receiving point in an environment, in which at least two transmitting points spaced apart from each other are present, each transmitting point having associated therewith a pilot sequence, wherein the pilot sequences are different from each other, comprising: a provider for providing an input signal, the input signal including a superposition of signals from the transmitting points; a transformer for transforming the input signal to obtain a transformed signal, the transformer being operative to apply a transform algorithm, which is based on a Fourier transform; a multiplier for providing a number of copies of the transformed signal, the number of copies being equal to the number of transmitting points; for each copy of the transformed signal, an extractor for extracting a portion of the copy of the transformed signal, the portion of the copy of the transformed signal representing an estimated channel impulse response for the channel to be estimated.
 10. A method for estimating a channel from a transmitting point to a receiving point in an environment, in which at least two transmitting points spaced apart from each other are present, each transmitting point having associated therewith a pilot sequence, wherein the pilot sequences are different from each other, comprising: providing an input signal, to a multplier the input signal including a superposition of signals from the transmitting points; using a multiplier to generate a number of copies of the input signal, the number of copies being equal to the number of transmitting points; for each copy of the input signal, transforming the copy or a signal derived from the copy to obtain a transformed signal by applying a transform algorithm, which is based on a Fourier transform; and for each transformed signal, extracting a portion of the transformed signal, using an extractor the portion of the transformed signal representing an estimated channel impulse response for the channel to be estimated, wherein only an associated transformed signal is used when extracting the portion of the transformed signal.
 11. A method for estimating a channel from a transmitting point to a receiving point in an environment, in which at least two transmitting points spaced apart from each other are present, each transmitting point having associated therewith a pilot sequence, wherein the pilot sequences are different from each other, comprising: providing an input signal, the input signal including a superposition of signals from the transmitting points; transforming the input signal to obtain a transformed signal by applying a transform algorithm, which is based on a Fourier transform; providing the transformed signal to a multiplier to generate a number of copies of the transformed signal, the number of copies of the transformed signal being equal to the number of transmitting points; and for each copy of the transformed signal, extracting a portion of the copy of the transformed signal, using an extractor the portion of the copy of the transformed signal representing an estimated channel impulse response for the channel to be estimated.
 12. A computer readable medium having stored thereon a computer program having a program code for performing a method for estimating a channel from a transmitting point to a receiving point in an environment, in which at least two transmitting points spaced apart from each other are present, each transmitting point having associated therewith a pilot sequence, wherein the pilot sequences are different from each other, comprising: providing an input signal, the input signal including a superposition of signals from the transmitting points; providing a number of copies of the input signal, the number of copies being equal to the number of transmitting points; for each copy of the input signal, transforming the copy or a signal derived from the copy to obtain a transformed signal by applying a transform algorithm, which is based on a Fourier transform; and for each transformed signal, extracting a portion of the transformed signal, the portion of the transformed signal representing an estimated channel impulse response for the channel to be estimated, wherein only an associated transformed signal is received used when extracting the portion of the tranformation signal, when the program runs on a computer
 13. A computer readable medium having stroed thereon a computer program having a program code for performing a method for estimating a channel from a transmitting point to a receiving point in an enviromental, in which at least two transmitting points spaced apart from each other are present, each transmitting having associated therewith a pilot sequence, wherein the pilot sequences are different from each other, comprising: providing an input signal, the input signal including a superposition of signals from the transmitting points; transforming the input signal to obtain a transformed signal by applying a transform algorithm, which is based on a Fourier transform; providing a number of copies of the transformed signal, the number of copies of the transformed signal being equal to the number of transmitting points; and for each copy of the transformed signal, extracting a portion of the copy transformed signal, the portion of the copy of the transformed signal representing an estimated channel impulse response for the channel to be estimated, when the program runs on a computer. 